There are 2 goods, apples (A) and bananas (B). The price of apples (bananas) is PA (PB). Preferences are represented
by the utility function U(DA,DB) = DA3 DB3 . If the consumer has income I, solving
the consumer’s maximization problem, we would get DA = 1I/PA and DB = 2I/PB. 33
Home’s endowment is 120 apples and 30 bananas.
(a) How many units of apples and bananas are consumed under autarky?
(b) What is the autarky relative price of bananas to apples PB/PA?
(c) Next, plot the autarky equilibrium, with apples on the y-axis and bananas on the x-axis.
(d) Introduce Foreign country with the same preferences. Foreign’s endowments are 60 apples and 60 bananas. Suppose the two countries open up to trade. What is the free trade relative price of bananas to apples (PB/PA)W ?
(e) Describe the world trade pattern: which country exports/imports what and how much. Confirm that export supply matches import demand for both goods.
(f) Using two separate graphs, plot the free trade equilibrium for Home and Foreign.
(g) Are both countries better off under free trade? Show graphically using the plot in part (f) as well as numerically.
(h) Suppose Foreign’s endowment of bananas increases, but its number of apples remains the same. Would the world trade pattern change? If so, how would it change?